Curious to know what metrics or strategies managers (and individual developers) are using to track productivity of individuals and teams. I'd like to get some ideas here for how best to do this myself
Check out the 4 key metrics from Accelerate - deployment frequency, lead time, change rate failure and mean time to recovery. This is good for teams. IMHO, tracking productivity for individuals is irrelevant.
I don't think anything exists out of the box unfortunately. You should be able to start tracking them manually as a starting point. Do read the book (Accelerate by Dr Nicole Forsgren) for more information about why these are important.